We report new multi-colour photometry and high-resolution spectroscopic observations of the long-period variable V501 Aur , previously considered to be a weak-lined T-Tauri star belonging to the Taurus-Auriga star-forming region .
The spectroscopic observations reveal that V501 Aur is a single-lined spectroscopic binary system with a 68.8-day orbital period , a slightly eccentric orbit ( e \sim 0.03 ) , and a systemic velocity discrepant from the mean of Taurus-Auriga .
The photometry shows quasi-periodic variations on a different , \sim 55-day timescale that we attribute to rotational modulation by spots .
No eclipses are seen .
The visible object is a rapidly rotating ( v \sin i \approx 25 ~ { } \mathrm { km } \mathrm { s } ^ { -1 } ) early K star , which along with the rotation period implies it must be large ( R > 26.3 ~ { } \mathrm { R } _ { \odot } ) , as suggested also by spectroscopic estimates indicating a low surface gravity .
The parallax from the Gaia mission and other independent estimates imply a distance much greater than the Taurus-Auriga region , consistent with the giant interpretation .
Taken together , this evidence together with a re-evaluation of the Li I \lambda 6707 and H \alpha lines shows that V501 Aur is not a T-Tauri star , but is instead a field binary with a giant primary far behind the Taurus-Auriga star-forming region .
The large mass function from the spectroscopic orbit and a comparison with stellar evolution models suggest the secondary may be an early-type main-sequence star .